Required plugins with depreciated functions

Hopefully this is a straight forward answer. If a theme is using TGM to install/activate a required plugin that uses depreciated functions in it’s most recent build. Will the theme be rejected by the review team?

Probably applies only to highly popular plugins. I don’t imagine reviewers testing all you’ve got there.
One thing to note is that they probably test your theme in the latest Wordpress available – If they got errors there, you are out!